Let's roll up our sleeves and solve this. We have 55 and we're going to multiply it by 111, essentially adding 55 to itself 111 times.
Step 1: 0 + 55 = 55
Step 2: 55 + 55 = 110
Step 3: 110 + 55 = 165
Step 4: 165 + 55 = 220
Step 5: 220 + 55 = 275
Step 6: 275 + 55 = 330
Step 7: 330 + 55 = 385
Step 8: 385 + 55 = 440
Step 9: 440 + 55 = 495
Step 10: 495 + 55 = 550
Step 11: 550 + 55 = 605
Step 12: 605 + 55 = 660
Step 13: 660 + 55 = 715
Step 14: 715 + 55 = 770
Step 15: 770 + 55 = 825
Step 16: 825 + 55 = 880
Step 17: 880 + 55 = 935
Step 18: 935 + 55 = 990
Step 19: 990 + 55 = 1045
Step 20: 1045 + 55 = 1100
Step 21: 1100 + 55 = 1155
Step 22: 1155 + 55 = 1210
Step 23: 1210 + 55 = 1265
Step 24: 1265 + 55 = 1320
Step 25: 1320 + 55 = 1375
Step 26: 1375 + 55 = 1430
Step 27: 1430 + 55 = 1485
Step 28: 1485 + 55 = 1540
Step 29: 1540 + 55 = 1595
Step 30: 1595 + 55 = 1650
Step 31: 1650 + 55 = 1705
Step 32: 1705 + 55 = 1760
Step 33: 1760 + 55 = 1815
Step 34: 1815 + 55 = 1870
Step 35: 1870 + 55 = 1925
Step 36: 1925 + 55 = 1980
Step 37: 1980 + 55 = 2035
Step 38: 2035 + 55 = 2090
Step 39: 2090 + 55 = 2145
Step 40: 2145 + 55 = 2200
Step 41: 2200 + 55 = 2255
Step 42: 2255 + 55 = 2310
Step 43: 2310 + 55 = 2365
Step 44: 2365 + 55 = 2420
Step 45: 2420 + 55 = 2475
Step 46: 2475 + 55 = 2530
Step 47: 2530 + 55 = 2585
Step 48: 2585 + 55 = 2640
Step 49: 2640 + 55 = 2695
Step 50: 2695 + 55 = 2750
Step 51: 2750 + 55 = 2805
Step 52: 2805 + 55 = 2860
Step 53: 2860 + 55 = 2915
Step 54: 2915 + 55 = 2970
Step 55: 2970 + 55 = 3025
Step 56: 3025 + 55 = 3080
Step 57: 3080 + 55 = 3135
Step 58: 3135 + 55 = 3190
Step 59: 3190 + 55 = 3245
Step 60: 3245 + 55 = 3300
Step 61: 3300 + 55 = 3355
Step 62: 3355 + 55 = 3410
Step 63: 3410 + 55 = 3465
Step 64: 3465 + 55 = 3520
Step 65: 3520 + 55 = 3575
Step 66: 3575 + 55 = 3630
Step 67: 3630 + 55 = 3685
Step 68: 3685 + 55 = 3740
Step 69: 3740 + 55 = 3795
Step 70: 3795 + 55 = 3850
Step 71: 3850 + 55 = 3905
Step 72: 3905 + 55 = 3960
Step 73: 3960 + 55 = 4015
Step 74: 4015 + 55 = 4070
Step 75: 4070 + 55 = 4125
Step 76: 4125 + 55 = 4180
Step 77: 4180 + 55 = 4235
Step 78: 4235 + 55 = 4290
Step 79: 4290 + 55 = 4345
Step 80: 4345 + 55 = 4400
Step 81: 4400 + 55 = 4455
Step 82: 4455 + 55 = 4510
Step 83: 4510 + 55 = 4565
Step 84: 4565 + 55 = 4620
Step 85: 4620 + 55 = 4675
Step 86: 4675 + 55 = 4730
Step 87: 4730 + 55 = 4785
Step 88: 4785 + 55 = 4840
Step 89: 4840 + 55 = 4895
Step 90: 4895 + 55 = 4950
Step 91: 4950 + 55 = 5005
Step 92: 5005 + 55 = 5060
Step 93: 5060 + 55 = 5115
Step 94: 5115 + 55 = 5170
Step 95: 5170 + 55 = 5225
Step 96: 5225 + 55 = 5280
Step 97: 5280 + 55 = 5335
Step 98: 5335 + 55 = 5390
Step 99: 5390 + 55 = 5445
Step 100: 5445 + 55 = 5500
Step 101: 5500 + 55 = 5555
Step 102: 5555 + 55 = 5610
Step 103: 5610 + 55 = 5665
Step 104: 5665 + 55 = 5720
Step 105: 5720 + 55 = 5775
Step 106: 5775 + 55 = 5830
Step 107: 5830 + 55 = 5885
Step 108: 5885 + 55 = 5940
Step 109: 5940 + 55 = 5995
Step 110: 5995 + 55 = 6050
Step 111: 6050 + 55 = 6105

So, 55*111 = 6105